Use the image to answer the question.

Question

Five labeled curves with bidirectional arrows are plotted on a coordinate plane.

Given the graph of f(x)
, which of the options is the graph of −f(x)
?

(1 point)
Responses

The graph of −f(x)
is option 3.
The graph of negative f left parenthesis x right parenthesis is option 3.

The graph of −f(x)
is option 2.
The graph of negative f left parenthesis x right parenthesis is option 2.

The graph of −f(x)
is option 1.
The graph of negative f left parenthesis x right parenthesis is option 1.

The graph of −f(x)
is option 4.

Answer 1

To determine which option represents the graph of \(-f(x)\), we need to understand that the graph of \(-f(x)\) is a reflection of the graph of \(f(x)\) across the x-axis.

1. If the original graph \(f(x)\) has points above the x-axis (positive values), then the graph of \(-f(x)\) will have those points reflected below the x-axis (negative values).
2. Conversely, if the original graph \(f(x)\) has points below the x-axis, those points will be reflected above the x-axis in the graph of \(-f(x)\).

Without viewing the specific curves, you would compare the given options to see which one shows the opposite orientation from the original graph of \(f(x)\).

If you can describe the characteristics of each option or how they relate to the original graph of \(f(x)\), I could assist you better in identifying which numbered option corresponds to the graph of \(-f(x)\).